Fazal ur Rehman

Robust Control of Underactuated Systems: Higher Order Integral Sliding Mode Approach

This paper presents a robust control design for the class of underactuated uncertain nonlinear systems. Either the nonlinear model of the underactuated systems is transformed into an input output form and then an integral manifold is devised for the control design purpose or an integral manifold is defined directly for the concerned class. Having defined the integral manifolds discontinuous control laws are designed which are capable of maintaining sliding mode from the very beginning. The closed loop stability of these systems is presented in an impressive way. The effectiveness and demand of the designed control laws are verified via the simulation and experimental results of ball and beam system.

A Comparative Experimental Study of Robust Sliding Mode Control Strategies for Underactuated Systems

This paper presents a comprehensive comparative study for the tracking control of a class of underactuated nonlinear uncertain systems. A given nonlinear model of the underactuated system is, at first stage, transformed into an input output form and the driving applied control input of the transformed system is then designed via four sliding mode control strategies, i.e., conventional first order sliding mode control, second order sliding mode, fast terminal sliding mode, and integral sliding mode. At second stage, a ball and beam system is considered and the aforementioned four control design strategies are experimentally implemented. A comprehensive comparative study of the simulation and experimental results is then conducted which take into account the tracking performance, i.e., settling time, overshoots, robustness enhancement, chattering reduction, sliding mode convergences, and control efforts.

Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode

This article presents a robust stabilizing control for nonholonomic underwater systems that are affected by uncertainties. The methodology is based on adaptive integral sliding mode control. Firstly, the original underwater system is transformed in a way that the new system has uncertainties in matched form. A change of coordinates is carried out for this purpose, and the nonholonomic system is transformed into chained form system with matched uncertainties. Secondly, the chained form system with uncertainties is transformed into a special structure containing nominal part and some unknown terms through input transformation. The unknown terms are computed adaptively. Afterward, the transformed system is stabilized using integral sliding mode control. The stabilizing controller for the transformed system is constructed which consists of the nominal control plus some compensator control. The compensator controller and the adaptive laws are derived in a way that the derivative of a suitable Lyapunov function becomes strictly negative. Two different cases of perturbation are considered including the bounded uncertainty present in any single control input and the uncertainties present in the overall system model of the underwater vehicle. Finally, simulation results show the validity and correctness of the proposed controllers for both cases of nonholonomic underwater system affected by uncertainties.

Adaptive Integral Sliding Mode Stabilization of Nonholonomic Drift-Free Systems

This article presents adaptive integral sliding mode control algorithm for the stabilization of nonholonomic drift-free systems. First the system is transformed, by using input transform, into a special structure containing a nominal part and some unknown terms which are computed adaptively. The transformed system is then stabilized using adaptive integral sliding mode control. The stabilizing controller for the transformed system is constructed that consists of the nominal control plus a compensator control. The compensator control and the adaptive laws are derived on the basis of Lyapunov stability theory. The proposed control algorithm is applied to three different nonholonomic drift-free systems: the unicycle model, the front wheel car model, and the mobile robot with trailer model. The controllability Lie algebra of the unicycle model contains Lie brackets of depth one, the model of a front wheel car contains Lie brackets of depths one and two, and the model of a mobile robot with trailer contains Lie brackets of depths one, two, and three. The effectiveness of the proposed control algorithm is verified through numerical simulations.

Smooth super-twisting sliding mode control for the class of underactuated systems

In this article, Smooth Super-twisting Sliding Mode Control (SSTWSMC) is investigated for the class of underactuated system. In underactuated systems, the control design is not directly applicable as for other systems (known as fully actuated systems). Therefore, at initial step, a nonlinear uncertain model of systems is transformed into the controllable canonical form, and then Smooth Super Twisting (SSTW) based Sliding Mode Control (SMC) is devised for the control design purpose for the considered class. In addition, closed loop stability of the proposed technique is presented in a fascinating way. The effectiveness and supremacy of the proposed control technique is proven by extensive analysis between conventional Sliding Mode Control (SMC), Super twisting (STW) sliding mode control and Smooth Super-twisting Sliding Mode Control (SSTWSMC). The comprehensive analysis evaluates the attributes like robustness enhancement, settling time, control effort, chattering reduction, overshoot, sliding mode convergence, etc. and is supported by simulations as well as practical implementation on ball and beam balancer (which is considered as application example).

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples.

Synchronization and Antisynchronization Between Two Non-Identical Chua Oscillators via Sliding Mode Control

This paper presents the synchronization and antisynchronization scheme between the Chua and modified Chua oscillators. Two cases are considered based on systems known and unknown parameters. In case of known parameters, synchronization and antisynchronization are achieved via sliding mode control, while in case of unknown parameters, adaptive integral sliding mode control is applied. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then, the error system is stabilized using integral sliding mode control. The stabilizing controller for the error system is constructed, which consists of the nominal control plus some compensator control. To avoid the chattering phenomenon, smooth continuous compensator control is used instead of traditional discontinuous control. The compensator controller and the adapted law are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. Numerical results are shown to illustrate and validate the synchronization schemes presented in this paper.